Five weeks after Pearl Harbor was attacked, Franklin Roosevelt received a handwritten letter from Kennesaw Mountain Landis, the former Tennessee judge who had been appointed by baseball owners in the wake of the 1919 “Black Sox” scandal to restore the sport’s reputation.

Would playing the 1942 season, Landis asked the president, help or hurt the war effort? “My dear Judge,” FDR replied the following day. “I honestly feel that it would be best for the country to keep baseball going.”

House Speaker Paul Ryan and Democratic House Leader Nancy Pelosi expressed similar sentiments Wednesday following the shooting at an Alexandria, Va., baseball field where Republicans were getting in their final practice for the annual congressional charity game at Nationals Stadium on Thursday.

In a closed-door meeting of House members, Ryan announced that Thursday’s game would still be played, generating spontaneous applause from Democrats and Republicans alike. Pelosi repeated this pledge in an emotional floor speech.

California Rep. Eric Swalwell tweeted:

The #congressionalbaseballgame is on. We will play for charity, but also for the victims & the heroic officers who took down the shooter.

That’s all as it should be. To not play the game would not be in the American tradition. At this moment in our history, however, it might not be enough. Although the annual game sometimes prompts some bipartisan comradery, it’s also competitive, as the game of baseball should be—under normal circumstances. But these are not normal circumstances, just as Wednesday’s shooting was not a normal crime.

The desire to win is why both the Democratic and Republican teams were practicing so early in the morning. Yet only one of two teams was attacked by a gunman who asked three minutes before the shooting started, “Are those Republicans or Democrats out there?”

Told that they were Republicans, this particular 66-year-old Bernie Sanders volunteer, Facebook fan of MSNBC, and confirmed Donald Trump hater apparently went to his vehicle, got his guns and started shooting at the defenseless ballplayers on the field. For his part, Sanders was appalled. “I am sickened by this despicable act,” said the Vermont senator. But as many lawmakers said during the day—and as Ryan and Pelosi suggested to their colleagues and the nation—the country needs more.

Speaking for the 40 percent of Americans who no longer identify with either party, something that transcends temporary shows of bipartisanship would be welcome. Pelosi made such a gesture Wednesday. From the House floor, while looking in the direction of the Republicans, she said she prays weekly for every member of Congress and for Donald Trump’s family—and even for a “successful” Trump presidency.

So, what would a gesture look like on the baseball diamond? Here’s a modest idea. Instead of Democrats competing against Republicans, how about choosing up sides the way American kids do on the schoolyard? Each team captain would pick a player, in order, and they must alternate picks, one Republican, then one Democrat. Don’t play against the other party, play with them—for this one night.

We’ve seen overtures like this before. Members stood on the Capitol steps and sang together on 9/11. For a while, they sat with an opposite-party buddy during the State of the Union address. Maybe this one could start a trend—a new kind of streak in a game that has been one of streaks. Before winning, 8-7, last year, the Republicans had lost seven annual congressional baseball games in a row. Prior to that, Democrats had dropped 11 of the previous 12.

At one point in the late 1950s, Sam Rayburn got so tired of Democrats losing that he cancelled the game under the pretext that members had more important things to do. From the beginning—and this game began in 1909—each party has been vigilant lest the other team bring in a ringer. The GOP figured out how to do it first: In 1968, North Carolina voters sent former St. Louis Cardinals and Pittsburgh Pirates pitcher Wilmer “Vinegar Bend” Mizell to Congress. Only six or seven years removed from the major leagues, Mizell proved unhittable for Democratic batters.

The Democratic manager is reported to have strode out to the mound with the following ultimatum: “If this guy throws one more pitch, we walk off the field.” And so, an unwritten rule was instituted: former pros can participate in the congressional game, but not at the position they played in the majors.

This tradition lasted until 1987, when the Republicans tried to avenge a loss the year before by trotting Jim Bunning out to the mound. He was freshman House member from Kentucky, and would also become an actual baseball Hall of Famer with a plaque in Cooperstown and everything. He was also 55 years old, however, and the Democrats ended up winning a wild game, 15-14. But who cares?

Winning an exhibition game is not what matters. What matters is that these people learn to work together. Maybe if they played together first, it would help. Rep. Rodney Davis, an Illinois Republican, seems to think so. Davis was at the plate taking batting practice Wednesday morning when the first shots rang out. He didn’t put the blame solely on a disturbed gunman. He faulted the vicious and overheated nature of our current national political discourse. “This hate has led to gunfire,” he said, his voice rising with emotion. “It has to stop.”

I’d like to see him bat for the Democrats Thursday night. Maybe that’s a place to start.

Carl M. Cannon is the Washington Bureau Chief for RealClearPolitics. Reach him on Twitter @CarlCannon.